Question Using Rolle's theorem for the following function, find all values \( c \) in the given interval where \( f^{\prime}(c)=0 \). If there are multiple values, separate them using a comma. \[ f(x)=2 x^{3}+\frac{45 x^{2}}{2}+21 x-2 \text { over }[-4,2] \] Provide your answer below: \[ =\square \]

1) \( f(x)=\sqrt{\frac{2}{\sqrt[x]{e 6 x+1}}} \)

Decide whether the following statement is true or false. The cube function is odd and is increasing on the interval \( (-\infty, \infty) \). Choose the correct answer below. False True

MAS182 - Applied Mathematics 13. Final Examination - S1 2021 The water content \( W(t) \) (measured in grams) in the cheese is governed by the differential equation \[ \frac{d W}{d t}=-(W-100)^{2} \] with initial condition \( W(0)=200 \mathrm{~g} \) and time is measured in hours.

Gegeben ist eine weitere Funktion h. mit der Gleichung \( h(x)=0,5 x^{3}-4 x^{2}+6 x+2 \) 74 a) Untersuchen Sie den Graphen von \( h \) auf mögliche Wendepunkte.

\( \lim _ { n \rightarrow + \infty } \frac { n ^ { 5 } + \sin n } { 3 ( \arctan n ) n ^ { 5 } } \)